Information feature analysis and improved algorithm of PCA

Principal component analysis (PCA) is an important method in multivariate statistical analysis, and its main idea is compression of dimensionality including variables and samples. In this paper, based on the ideas concerned with information function and information entropy of Shannon information theory, consider the inherent characteristic of eigenvalues of matrix, two new concepts of possibility information function (PIF) and possibility information entropy (PIE) are proposed firstly. On the basis of these, the formulae of information rate (IR) and accumulated information rate (AIR) are set up, by which the degree of information compression is measured. In the end, we improve the PCA algorithm called improved principal component analysis (PCA). Through simulated application in practice, the results show that the IPCA proposed here is efficient and satisfactory. It provides a new research approach of information feature compression for pattern recognition.